Please explain what you are to do with these.
It is not clear what is going on.
What does contrapositive have to do with these.
1. If pq is odd, then p is odd and q is odd.
for this one, I had already proved that if p is odd and q is odd then pq is odd.
So in relation to this question i proved that q => p, so with a truth table I used that since p&q are the same(odd) then the reverse(p=>q) is also true.
does that sound alright?
2. if p^2 is even, then p is even.
This one im not quite sure how to prove ive tried the contrapositive:
so if p^2 is not even, the p is not even.
I substituted for p 2k+1, and tried setting it equal to 2k + 1 but my answer doesnt really make sense to me.
any help?
Please don't use the same letters to mean the same thing! You start by talking about p and q being odd, implying that they are integers. You then talk about p&q and p=>q implying that they are statements. Which is it?
And you give a statement, "If pq is odd, then p is odd and q is odd", but don't say what you want to do with it! Prove it? Find the contrapositive of it?
Proof by contradiction. Suppose p is odd. Then p= 2k+1 as you say. What is its square?does that sound alright?
2. if p^2 is even, then p is even.
This one im not quite sure how to prove ive tried the contrapositive:
so if p^2 is not even, the p is not even.
I substituted for p 2k+1, and tried setting it equal to 2k + 1 but my answer doesnt really make sense to me.
any help?